# 8.3: Definition of Reaction Rate

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If one assumes that the batch reactor shown in Figure \(8.2.1\) is *perfectly mixed*, Equation (\(8.2.4\)) takes the form

\[\frac{dc_{A} }{dt} =R_{A} ,\left\{\begin{array}{c} \text{perfectly mixed,} \\ \text{constant volume} \\ \text{ batch reactor} \end{array}\right\} \label{34}\]

Often there is a tendency to think of this result as defining^{4} the “reaction rate” and this is a perspective that one must avoid. Equation \ref{34} represents a special form of the *macroscopic mole balance for species* \(A\) and it does not represent a *definition* of \(R_{A}\). In reality, Equation \ref{34} represents a very attractive special case that can be used with laboratory measurements to determine the *net molar rate of production* of species \(A\), \(R_{A}\). Once \(R_{A}\) has been determined experimentally, one can search for chemical kinetic rate expressions such as that given by Eq. (\(8.2.9\)), and details of that search procedure are described in Chapter 9. If successful, this search provides both a satisfactory form of the rate expression and it provides reliable values of the parameters that appear in the rate expression. To be convinced that Equation \ref{34} is not a definition of the reaction rate, one need only consider the perfectly mixed version of Equation (\(8.2.3\)) which is given by

\[\frac{dc_{A} }{dt} + \frac{c_{A} }{\mathscr{V}(t)} \frac{d\mathscr{V}(t)}{dt} =R_{A} ,\left\{\begin{array}{c} \text{perfectly mixed,} \\ \text{ batch reactor} \end{array}\right\} \label{35}\]

Here it should be clear that \(R_{A}\) is *not defined* by \(dc_{A} /dt\); rather \(R_{A}\) is an *intrinsic property* of the system that represents the net molar rate of production of species \(A\) per unit volume. This is the sense in which the rate of production was introduced in Chapter 4.